标题： XY量子自旋链的熵涨落 显示英文标题

标题： Entropic fluctuations of XY quantum spin chains

摘要： 我们考虑一个XY量子自旋链，它由左、中和右三部分组成，初始时分别处于温度$T_l$、$T_c$和$T_r$的热平衡状态。左边和右边的系统是无限扩展的热库，而中间的系统是一个连接这两个热库的小型量子系统。如果存在温度差，则热量和熵会从链的一个部分流向另一个部分。我们考虑Evans-Searles和Gallavotti-Cohen泛函，这些泛函描述了这种通量相对于系统初始状态和系统在长时间极限下达到的非平衡稳态的波动情况。我们还定义了XY链的完整计数统计，并考虑相关的熵泛函，以及一种自然的泛函类，这些泛函在完整计数统计泛函和经典非平衡统计力学中出现的Evans-Searles泛函的直接量化变分特征之间进行插值。Jordan-Wigner变换将一个自由费米气体和雅可比矩阵与我们的XY链相关联。利用这种表示，我们能够根据底层雅可比矩阵的散射数据，在长时间极限下计算熵泛函。我们证明在该极限下，Gallavotti-Cohen和Evans-Searles泛函是相同的。此外，我们证明如果底层雅可比矩阵是无反射的，则所有这些熵泛函在长时间极限下都相等。 显示英文摘要

摘要： We consider an XY quantum spin chain that consists of a left, center and right part initially at thermal equilibrium at temperatures $T_l$, $T_c$, and $T_r$, respectively. The left and right systems are infinitely extended thermal reservoirs and the central system is a small quantum system linking these two reservoirs. If there is a temperature differential, then heat and entropy will flow from one part of the chain to the other. We consider the Evans-Searles and Gallavotti-Cohen functionals which describe the fluctuations of this flux with respect to the initial state of the system and the non-equilibrium steady state reached by the system in the large time limit. We also define the full counting statistics for the XY chain and consider the associated entropic functional, as well a natural class of functionals that interpolate between the full counting statistics functional and the direct quantization of the variational characterization of the Evans-Searles functional which appears in classical non-equilibrium statistical mechanics. The Jordan-Wigner transformation associates a free Fermi gas and Jacobi matrix to our XY chain. Using this representation we are able to compute the entropic functionals in the large time limit in terms of the scattering data of the underlying Jacobi matrix. We show that the Gallavotti-Cohen and Evans-Searles functionals are identical in this limit. Furthermore, we show that all of these entropic functionals are equal in the large time limit if and only if the underlying Jacobi matrix is reflectionless.